Removal of fluoride from contaminated groundwater by cross flow nanofiltration: Transport modeling and economic evaluation

Desalination 313 (2013) 115–124

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Removal of fluoride from contaminated groundwater by cross flow nanofiltration: Transport modeling and economic evaluation S. Chakrabortty a, M. Roy b, P. Pal a,⁎ a b

Environment and Membrane Technology Laboratory, Department of Chemical Engineering, National Institute of Technology Durgapur 713209, India Department of Management Studies, National Institute of Technology Durgapur 713209, India

H I G H L I G H T S ► ► ► ►

Mathematical model developed for fluoride separation by nanofiltration Model has successfully predicted the system performance with less than 0.1 relative errors. The system has been found to remove more than 98% of fluoride from water. Achieved flux was reasonably high for industrial acceptance.

a r t i c l e

i n f o

Article history: Received 8 September 2012 Received in revised form 5 December 2012 Accepted 18 December 2012 Available online 16 January 2013 Keywords: Fluoride removal Cross-flow module Membrane fouling Nanofiltration modeling

a b s t r a c t A modeling and simulation study along with economic evaluation was carried out for removal of fluoride from contaminated groundwater in a flat sheet cross flow nanofiltration membrane module. Mathematical model was developed based on extended Nernst–Planck equation and with the help of ‘concentration polarization modulus’ equation. Linearized approach in modeling reduced computation time significantly. Effects of transmembrane pressure, cross-flow rate, pH and concentration of the solute of interest on membrane charge density, solute rejection and solvent flux were investigated. The membrane module was successful in yielding a pure water flux as high as 158 l m−2 h−1 removing more than 98% of the fluoride at a transmembrane pressure of only 14 kgf cm−2 and at a pH of 10.01 for a volumetric cross flow rate of 750 L h−1. The membrane module not only removed fluoride effectively but also brought down high pH of groundwater to the desired level. The developed model corroborated well with the experimental findings as reflected in the very low relative error (b 0.1) and high value of overall correlation coefficient (R2 > 0.98). Economic analysis indicated that such a membrane filtration system could be quite promising in purifying fluoride-contaminated groundwater at low cost. © 2012 Elsevier B.V. All rights reserved.

1. Introduction High fluoride concentration in drinking water has been found to cause severe human health hazards. Fluoride occurs in groundwater in the form of fluorine, biotite, cryolite, fluoro-apatite and villiaumite (NaF) [1,2]. The problem of high fluoride concentration in groundwater resources has now become one of the most serious toxicological and geo environmental issues in several countries featuring India as the most dominant one. Over the last three decades, the high fluoride concentration in drinking water and the resultant disease ‘fluorosis’ have been highlighted considerably throughout the world. Intake of excess fluoride (>10 ppm) in the human body may cause dental, skeletal and non-skeletal ‘fluorosis’. Again lack of fluoride in groundwater (less than 0.5 ppm) may cause dental caries [3]. WHO has already recommended the highest desirable and maximum permissible contaminant level (MCL) of fluoride in drinking water to be 1 ppm ⁎ Corresponding author. Tel.: +919434469750; fax: +913432547375. E-mail address: [email protected] (P. Pal). 0011-9164/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.desal.2012.12.021

and 1.5 ppm respectively with the consideration of proper safeguard limit of fluoride in drinking water [4]. This has thrown a challenge to the scientific community to purify water with extremely high degree of efficiency to bring down concentration of fluoride to the safe limit where groundwater has been found to contain twenty times the permissible limits. Occurrence of fluoride in groundwater and the related problems of contaminated drinking water have been widely published [5–9]. Technologies such as precipitation, adsorption, and ion exchange [10–14] have been well studied for separation of fluoride from contaminated groundwater. Membrane based technologies such as electro dialysis, reverse osmosis and nanofiltration have also been examined and identified [15–18] in the recent years as the potential technologies for fluoride separation from contaminated drinking water. Among these membrane processes, nanofiltration stands to be one the most effective technologies as it can remove a number of other contaminants also from groundwater at a relatively low transmembrane pressure using low priced membranes. Nanofiltration (NF) membranes which have the operational properties in between those of ultrafiltration membranes and

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reverse-osmosis membranes possess the potential of high degree of fluoride separation at relatively lower operating pressure than reverse osmosis (RO) while permitting higher fluxes than reverse osmosis and significantly better rejection than ultrafiltration. Separation of the impurities by nanofiltration membranes may exploit both steric (sieving) and Donnan (electrical) mechanisms depending on the characteristics of such impurities. Lower pumping cost and membrane cost compared to those of the reverse osmosis membranes often make nanofiltration a more economically and operationally attractive option. Reported studies [19–22] on nanofiltration for fluoride separation from water have largely been on experimental investigations using mainly spiral wound or hollow fiber modules where fouling still remains a major concern. Modeling and economic feasibility studies are very scanty resulting in lack of scale up confidence. To our knowledge, no modeling, simulation and economic feasibility study has been reported on cross flow nanofiltration membrane module for fluoride separation despite its potential of offering largely fouling-free operation in a very simple module and at a relatively low price. The present study intends to fill this gap.

The flux (Js) of ion i is the sum of the fluxes due to convection, diffusion and electro migration. Ds,i is the diffusion coefficient of i through the membrane pores which accounts for the component friction with the pore walls, Hc,i are the hindrance factors for convection. Again the solute flux can be described by the equation J S;i ¼ V  C p;i

where V is the solvent velocity and it may be expressed using Hagen– Poiseuille type equation as

V¼

rp 2 ΔPe 8ηΔx

2.1. Model assumptions 1. The effective membrane charge density (XDC) is constant throughout the membrane and is mainly controlled by the concentration of the solution and pH of the feed solution. 2. The nanofiltration membrane consists of a bundle of identical straight cylindrical pores with uniform radius (rp) and length Δx (with Δx > > rp). 3. The steric effect in the Donnan partitioning at the interface of the membrane is negligible. 4. The solute Concentration and electric potential inside the membrane are all defined in terms of radially averaged quantities. 5. Osmotic pressure difference (Δπ) may be assumed to be insignificant due to relatively low concentration of fluoride in contaminated groundwater. 6. Salvation barrier energy (ΔWi) may be neglected to avoid complexity of computation. 7. Membrane wall concentration of the charged solute varies with time and for a long time operation. 2.2. Model equations With the help of the basic assumptions as described in the previous section, the mathematical model was developed. The flux for charged particle through the nanofiltration (NF) membrane can be measured using extended Nernst–Planck equation [25–27]. That modified Nernst–Planck equation can describe transport of negatively charged ions has been well illustrated by Pal et al. [33] in determination of arsenic rejection (H2AsO4−). In the present investigation, transport of fluoride ions (F−) through NF membrane may be expressed as:

  
  dcw;i zi cW;i Ds;i F dψ : − Js;i ¼ Hc;i cW;i V − Ds;i dx dx RT

ð1Þ

! ð3Þ

ΔPeis termed as effective pressure driving force and it is expressed as ΔPe = dp = (Δp − Δπ). The concentration gradient for fluoride ion can be derived by help of Eq. (1) incorporating Eq. (2) in Eq. (1) and it can be expressed as

2. Theoretical aspects and model development In nanofiltration process, the solute particles are separated by steric (size) and Donnan (electrical) exclusion mechanisms [23,24]. Extended Nernst–Planck model [25] adequately describes separation of ionic or charged solute particles. Extended Nernst–Planck equation together with concentration polarization models can adequately describe fouling behaviors of nanofiltration membranes and with this basic understanding, the present model has been developed with the assumptions as listed below.

ð2Þ

dcW;F ¼ dx

      V Hc;F cW;F −V Cp;F F zF cW;F dψ :  − dx DF RT

ð4Þ

The potential gradient through the membrane can be derived with the help of three equations (Eqs. (1), (2) and (4)) and it may be expressed as:
3 2
31 02 zNa V Hc;Na cW;Na −Cp;Na zF V Hc;F cW;F −Cp;F 5þ4 5C B4 B C DNa DF C dψ B C
 ¼B B C 2 2 dx B C zNa cW;Na þ zF cW;F @ A  

 RT : F

ð5Þ

The electro neutrality conditions within the pore and the permeate solutions are
 zNa cW;Na þ zF cW;F ¼ −X DC

ð6Þ

zNa Cp;Na ¼ −zF Cp;F

ð7Þ

where, XDC = membrane charge density, mol m −3. Applying the electro neutrality conditions (Eqs. (6) and (7)) cw,Na and Cp,Na may be substituted into Eq. (5) and substitution of solvent velocity in the same equation yields:      0H Cp;F Cp;F Hc;F cW;F Hc;Na XDC 1 c;Na cW;F − − − − C dψ B DNa DF DNa D DNa C
 F ¼B A dx @ 2cW;F −XDC   VR T :  F

ð8Þ

The membrane wall concentration of both ions can be measured by the Donnan equilibrium condition (Neglecting salvation energy barrier) which is expressed as:  
 −zi F Δψd cw;i ¼ CBC;i φi exp : RT

ð9Þ

S. Chakrabortty et al. / Desalination 313 (2013) 115–124

Substitution cw,Na of Eq. (6) into Eq. (8) and substitution of Eq. (8) into Eq. (4) results in the following relation: 2H

c;Na

dcW;F 6 ¼6 4 dx

DNa

þ

Hc;F DF



  
 c cW;F Cp;F Cp;F XDC 3 W;F Cp;F 2  cW;F −XDC cW;F − þ þ 7 D DF DF 7
 Na 5 2cW;F −XDC

 V:

ð10Þ

As the above equation holds for a higher order numerator than the denominator so the concentration gradient will be effectively constant and it shows that the effect of cw,F term is relatively small. Under these conditions, the concentration gradient can be approximated as follows: 2H ΔcW;F 6 ¼6 4 Δx

c;Na

DNa

þ

Hc;F DF



  
 c cW;Fav Cp;F Cp;F XDC 3 W;Fav Cp;F 2 þ  cW;Fav −XDC cW;Fav − þ 7 DNa DF DF 7
 5 2cW;Fav −XDC

 V:

Δψd ð0Þ ¼

          cW;Na ð0Þ cW;F ð0Þ RT RT  ln  ln ¼ : − F F φNa CBC φF CBC

Pei ¼

! Hc;i VΔx : Ds;i

ð12Þ

ð13Þ

ð19Þ

Rejection is calculated by the following expression Rj;F ¼

! Cp;F 1− : CBC;F

ð20Þ

The membrane wall concentration (cw) of the solute can be measured by the ‘concentration polarization’ model equation which is changed with the operating time. So the equation may be described as a function time.

ð11Þ

Algebraic manipulation of Eq. (12) with Eq. (5) yields the following equation
2
 2 cW;F −XDC þXDC cW;F −XDC −φNa :φF :CF ¼ 0:

where Peclet number, Pei is defined by the Hagen–Poiseuille definition and it is expressed as

cw;F ðtÞ ¼

The Donnan potential at the pore inlet (x = 0) is the same for both ions and it is obtained from Eq. (9)

117


  
   Js 1−Rj;F þ Rj;F :exp  CBC;F : kmass

ð21Þ

As the system is a cross-flow system, cross-flow velocity is expected to be an important parameter for the present model and particularly for the flux calculation during a long term operation. So the membrane wall concentration is dependent on cross flow velocity of the system and the operation time. The modified equation for the present cross flow system may be described as: cw;F ðv; tÞ ¼




  
   Js 1−Rj;F þ Rj;F :exp  CBC;F : kmass

ð22Þ

The calculated membrane wall concentration (cw,F) is then used in above equations for further calculation.

The above equation yields two roots which were formed as per changed concentration of fluoride and the two roots are:

2.3. Determination of physico-chemical parameters

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r
0 1 X þ X2DC þ4 φNa φF C2BC;F C B DC C: cW;F ð0Þ ¼ B @ A 2

The physico-chemical parameters of the model equations were computed by empirical relations as described below. ð14Þ

Similarly, an equivalent quadratic expression at the pore outlet (x = Δ x) gives ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r
0 1 2 2 X þ X þ4 φ φ C DC Na F p;F C DC B C: cW;F ðΔxÞ ¼ B @ A 2

ð15Þ

2.3.1. Computation of pore radius (rp) and effective membrane thickness (Δx) Membrane pore radius (rp) and effective membrane thickness (Δx) were calculated by the validation of the rejection and flux data with the experimental value by the separation of uncharged solutes (sucrose). 2.3.2. Determination of hindered diffusivity (Ds,i) Hindered diffusivity (Ds,i) is the product of bulk diffusion coefficient (DBC) and hindered diffusivity (HD,i), which is expressed as:

Here cW,F (Δx) is calculated with a guess value of Cp,F and the guess value is checked with a new Cp,F value from Eq. (18).

DS;i ¼ DBC HD;i

h i ΔcW;F ¼ cW;F ðΔxÞ−cW;F ð0Þ

where hindered diffusivity (HD,i) is expressed as:

cW;Fav

  cW;F ð0Þ þ cW;F ðΔxÞ ¼ 2

ð16Þ ð17Þ

Rearrangement of Eq. (11) and yields the following explicit expression for Cp,F


 2 3 HD;i ¼ 1:0−2:3λi þ 1:154λi þ 0:224λi and λi ¼

2.3.3. Determination of Peclet number (Pei) Peclet number is defined by the help of below equation

2

Cp;F

3 h
i h i h
 i 2 6 ðPe þPe Þ  X c 7 ð þPe Þ  c −X − Pe þ 2c  Δc 6 W;Fav Na F DC W;Fav Na F W;Fav DC W;F 7 7 ! ! ¼6 6 7 PeNa cW;Fav PeF cW;Fav PeF XDC 4 5 − þ Hc;F Hc;Na Hc;F

ð18Þ

! rs;i : rp

Pe;i ¼

Hc;i :V:Δx DS;i

!

where φi = (1 − λi) 2.

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Table 1 Typical set of model parameters used in computation. Parameter

Value

Pore radius of NF-1 membrane Pore radius of NF-2 membrane Pore radius of NF-20 membrane Temperature maintained in units (T) Feed water flow rate Cross flow velocity Operating temperature Operating pressure Solution velocity pH in the oxidant unit Solute radius of Na+ ion (rs,Na) Solute radius of F− ion (rs,F) Bulk diffusivity of Na+ ion (DNa) Bulk diffusivity of F− ion (DF) Mass transfer coefficient of fluoride ion Boltzmann constant (k) Faraday's constant

0.53 × 10−9 m 0.57 × 10−9 m 0.54 × 10−9 m 308 K 750 L h−1 1.25 m s−1 308 K 14 kgf cm−2 0.95 × 10−3 kg m−1 s−1 10.01 0.116 × 10−9 m 0.119 × 10−9 m 1.9 × 10−9 m2s−1 4 × 10−10m2s−1 5.06 × 10−2 m s−1 1.38066 × 10−25 J K−1 96,485 C mol−1

2.4. Computation procedure The membrane charge density was predicted by this model calculation with validate of experimental data with model predicted data. Typical model parameters as used in the computation have been presented in Table 1. Concentration polarization model, another new approach has been introduced for the calculation of fouling model data. The model was developed by the following steps as described below. 1. First step for the calculation of model predictive value was membrane surface concentrations calculation and it was computed using Eq. (9) for both ions [Na + and F −]. 2. Eq. (14) was then used to calculate cW,F(0) with a known feed concentration (CBC,F) and Eq. (15) was used to find cW,F(x) with an assumed permeate concentration (Cp,F) value. 3. ΔcW,F and cW;Fav were computed using Eqs. (16) and (17) and checking the guess value of Cp,F using Eq. (18). 4. Fluoride separation was then calculated using Eq. (20) where volumetric flux of the solvent was calculated using Eq. (1). 5. An iterative method was adopted to compute rejection and flux using some assumed value of surface charge density (XDC) till the assumed value converged with the experimental value. 6. After the calculation of fluoride rejection and solvent flux this data were used for membrane wall concentration by the using of concentration polarization modulus (Eq. (21)). 7. This membrane wall concentration depends on the operation time and cross-flow velocity. So with change of operation time, the membrane wall concentration was also changed. This changed value was then used as the membrane surface concentration of solute for further model calculation which was computed before by the help of Eq. (9).

3. Materials and methods 3.1. Standards, reagents and membranes All the chemicals reagents were of reagent grade and no further purification was done. Fluoride standards (1000 ppm), Sodium (1000 ppm), chloride (1000 ppm), NaOH and concentrated HCl are purchased from E. Merck, Germany. Thin film composite polyamide nanofiltration (NF-1, NF-2 and NF-20) was procured from Sepro Membranes Inc. (USA). The active membrane surface area is 100 cm 2. The main characteristics of the nanofiltration membranes are listed in Table 2.

Table 2 Membrane characteristics and its performance at 10 kgf cm−2operating pressure (at 7 pH). Characteristics

NF-1

NF-2

NF-20

Membrane geometry Membrane materials Thickness (cm) Maxim Temp (K) pH resistance Solute rejection (%) MgSO4 NaCl Water Flux (L h−1 m−2) Investigated Flux (L h−1 m−2) Fluoride rejection (%)

Flat-sheet Polyamides 0.0165 323 2–11

Flat-sheet Polyamides 0.0165 323 2–11

Flat-sheet Polyamides 0.0165 323 2–11

99.5 90 110 106 95

97 50 130 124 78

98 35 120 116 86

3.2. Groundwater sampling and characterization Investigations were carried out with a flat sheet cross flow membrane module possessing the ability to resist fouling to a large extent. All experiments were conducted with fluoride contaminated groundwater collected from some fluoride-affected areas of Eastern India (Asanjola village, Rampurhat block1, Birbhum, West Bengal, India) and concentration of fluoride was found to be around 20 ppm. Fluoride, chloride, sodium, pH, salinity, conductivity and total dissolved solids (TDS) were determined by Orion 4 star ISE bench top ion meter with respective electrodes (Thermo Electron Corporation, USA) where iron was determined by atomic absorption spectrophotometer (AAS100, Perkin Elmer). Physico-chemical characterization of this groundwater has been presented in Table 3. 3.3. Experimental setup The experimental set up consists of a stirred stainless steel feed reactor and two parallel cross flow membrane modules along with necessary accessories for monitoring flow, pH, temperature and pressure. Feed was circulated through the membrane modules by a reciprocating pump (Milton Roy Pvt. Ltd.). A bypass valve, a rotameter and a pressure indicator were used to maintain and regulate the transmembrane pressure and desired cross flow. Initially the system was run for 1 h with deionized water for compaction of the nanofiltration membranes. Schematic diagram of the nanofiltration experimental setup has been shown in Fig. 1. 3.4. Experimental procedure All experiments were conducted in continuous flow mode. Effective membrane filtration surface of each membrane module was 100 cm2. Investigations were carried out at different pressures (5, 8, 11, 14 and 16 kgf cm−2), cross flow rates, different pH values, fluoride concentrations and different concentrations of other ions like iron. Pure water flux and solute rejection steadily increased as transmembrane pressure was increased from 5 to 16 kgf/cm 2. However, beyond a transmembrane pressure of 14 kgf/cm2, further gains in terms of pure water flux and Table 3 Groundwater characteristics for sample taken from fluoride affected village in Birbhum district. Parameters

Measured amount

Salinity Conductivity pH TDS Fluoride Chloride Sodium Iron

0.11 671 μS/cm 10.01 325 mg/L 20 mg/L 82 mg/L 355 mg/L 0.7 mg/L

S. Chakrabortty et al. / Desalination 313 (2013) 115–124

119

Recycle Stream

Rotameter

pH probe

Make up feed water Stirrer

Pressure Gauge

Pump Feed

Bypass Valve

Pressure Gauge

Membrane

Reciprocating pump

Module

Permeate

Groundwater

Fig. 1. Schematic diagram of the cross flow nanofiltration module used in investigation.

solute rejection were almost negligible. Permeate samples were analyzed at definite time intervals for checking rejection. Flux was continuously measured using high precision electronic balance. 3.5. Analytics Analysis of fluoride has been carried out in Orion 4 star pH ISE Bench top Ion Meter of Thermo Electron Corporation, USA. The Ion meter was first calibrated using the previously prepared fluoride samples of known strength. Removal efficiency of fluoride was calculated using the bulk fluoride concentration (CBC,F) which is present in feed sample and the residual concentration (CP,F) in the permeate respectively by the below equation: % of fluoride rejection ¼

1−

CP;F CBC;F

!  100:

3.6. Analysis of membrane morphology Membrane morphology was examined by Scanning Electron Microscopy (SEM, Hitachi S-3000N, Japan) before and after each experiment to find out the extent of membrane fouling. Degree of fouling was also cross checked through flux measurement. Prior to each SEM analysis, membrane pieces were freeze-fractured in liquid nitrogen and then coated with gold in ion sputter. SEM analysis was conducted at15kV for the surfaces of the membranes. 3.7. Error analysis and model performance

where Ei = experimental value, Pi = predicted (model) value, n = no of points analysis, Relative error (RE) was then calculated as, RE ¼ RMSE where, Ē = mean of experimental data. A very good model perE formance is indicated if R 2 > 0.98 and REb 0.10. The performance of the model has been presented in Table 4 that checked the model performance for each membrane with fluoride rejection data. 4. Results and discussion 4.1. Flux behavior during nanofiltration under varying operating pressure The experimental flux data as well as model data as presented in Fig. 2 show that permeate flux increases with transmembrane pressure from 5 kgf cm −2 to 16 kgf cm −2 for all the different membranes and it was found that flux varied linearly with applied pressure. Such flux behavior of the nanofiltration membranes with pressure during investigation is well established in the literature [18]. Results of investigations suggest that NF-2 is the loosest type as it produces the maximum flux compared to the other two membranes, whereas NF-1 is the tightest membrane yielding the lowest flux at the same operating conditions. At 14 kgf cm−2 pressure, the flux of NF-1 membrane attained as high as158 L h−1 m −2 which is reasonably high for

Table 4 RE and R2 value for volumetric flux, rejection estimated by the three NF membranes under different conditions.

Error analysis was done using standard statistical method that consisted of computation of certain parameters as described below. 1 First of all Root mean square error (RMSE) was calculated as

RMSE ¼

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX n u 2 u ðPi Ei Þ t i¼1

n

NF-1

Fig. Fig. Fig. Fig. Fig.

2 3 7 8 10

NF-2

NF-20

RE

R2

RE

R2

RE

R2

0.012 0.030 0.041 0.072 0.022

0.993 0.999 0.990 0.976 0.991

0.060 0.074 0.084 0.083 0.052

0.992 0.991 0.982 0.971 0.988

0.057 0.050 0.066 0.074 0.034

0.992 0.995 0.989 0.979 0.990

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S. Chakrabortty et al. / Desalination 313 (2013) 115–124 Table 5 Membrane charge density (XDC) obtained from the linearized model of different membranes.

Fig. 2. Effect of transmembrane pressure on flux through NF1, NF2 and NF20 membranes. Operating conditions: fluoride concentration 20 ppm, pH 10, pressure range 5 kgf cm−2–16 kgf cm−2, cross flow rate 750 L h−1, cross flow velocity 1.16 m s−1, temperature 308 K.

Membrane

Membrane charge density (XDC, mol/m3)

NF-1 NF-2 NF-20

−65.5 −16.5 −36.9

flux (fluoride ion) remains constant and due to the low concentration of the solutes in the permeate side, the overall solute passage decreases. This implies that rejection of a solute of interest increases with increase in transmembrane pressure. In the size exclusion mechanism, relative sizes of the membrane pore and solute dimension assume important role in determining degree of separation. Electrostatic charge repulsion between negatively charged membrane surface and the negative solute ions enhances the fluoride retention from groundwater. Model predictions on rejection here quite satisfactorily corroborate with experimental data. The error calculation of these rejection data as shown in the previous section was also quite satisfactory.

industrial acceptance. The model predictions corroborated well with the experimental observations.

4.3. Effect of cross flow rate on permeate flux and rejection during investigation

4.2. Removal performance of fluoride under varying pressure A steady increase in fluoride rejection was observed for all the tested membranes with increase of transmembrane pressure. However, beyond 14 kgf cm−2, further improvement in fluoride rejection was negligible. So an operating pressure of 14 kgf cm−2 was considered as the optimum pressure. Fig. 3 shows that NF-1 has the highest fluoride rejection capability (98.5%) whereas NF-2 shows the least rejection capability (91%). Same rejection behavior was shown by these three membranes in some previous studies [28,29]. Present investigation results illustrate that the rejection capability of the membranes follows the order NF-1 > NF-20 >NF-2 at any applied pressure. The investigation data were fitted with the linearized model in order to obtain the effective membrane charge density (XDC) which is shown in Table 5. Two transport mechanisms may work during fluoride rejection of NF membranes. Solution–diffusion mechanism is one of the transport mechanisms of a NF membrane where solute flux and solvent flux are uncoupled and as a result, with the increase of applied pressure, solvent flux increases without corresponding increase of solute flux [28]. So with increasing pressure, pure water flux increases, while the solute

A significant effect of cross flow rate on permeate flux was observed during nanofiltration of fluoride-contaminated groundwater. In quite a few studies [28], positive correlation between flux and cross flow rate has been well established. The flux data have been shown in Fig. 4 (secondary axis) which indicates that the flux increases with increasing cross flow rate from 300 L h−1 to 750 L h−1 at a constant pressure 14 kgf cm−2 for all the three membranes. NF-2 membrane produces a high permeate flux of 365 L/m 2 H at a cross flow rate of 750 L h−1 whereas NF-1 membrane produces a far less flux of 158 L h−1 m−2 and NF-20 produced an intermediate permeate flux of 214 L h−1 m−2 under the same operating conditions. Large pore radius of NF-2 membrane helped to provide much more flux than the other two membranes and the lowest permeate flux of NF-1 indicates its tightest nature. A significant role is played by cross flow rate to reduce the concentration polarization by virtue of its sweeping action on the membrane surface and thus reducing fouling. The rejection data ad presented in Fig. 5 shows that the fluoride rejection increases with the increasing crossflow rate from 300 L h−1 to 750 L h−1 for all the nanofiltration membranes and it is found that for NF-1 membrane, rejection increases from 93.8% to 98.5% with the increase of cross-flow rate from

Fig. 3. Effect of transmembrane pressure on fluoride removal through NF1, NF2 and NF20 membranes. Operating conditions: Fluoride concentration 20 ppm, pH 10, pressure range 5 kgf cm−2–16 kgf cm−2, cross flow rate 750 L h−1, cross flow velocity 1.16 m s−1, temperature 308 K.

Fig. 4. Effect of cross flow rate on permeates flux and rejection through NF1, NF2 and NF20 membranes. Operating conditions: fluoride concentration 20 ppm, pH 10, cross flow rate range 300–750 L h−1, pressure— 14 kgf cm−2, temperature 308 K.

S. Chakrabortty et al. / Desalination 313 (2013) 115–124

Fig. 5. Effect of pH on fluoride rejection and flux through NF1, NF2 and NF20 membranes. Operating conditions: fluoride concentration 20 ppm, pH range 2–10.01, cross flow rate 750 L h−1, pressure-14 kgf cm−2, cross flow velocity 1.16 m s−1, temperature 308 K.

300 L h−1 to 750 L h−1. It also displays the highest rejection capability whereas NF-2 carries the lowest rejection characteristic. The increasing cross-flow rate creates a sweeping action on the active membrane surface area which reduces the effect of concentration polarization leading to a fouling-free nature. As a result of which, higher degree of separation could be achieved due to the achievement of maximum available effective membrane surface area for separation. Again reduction of concentration polarization enhances convective force that in turn enhances the solvent flux. Uncoupling nature of the solute and solvent fluxes also results in higher retention of fluoride in this case. Fig. 4 shows that in case of NF-2 and NF-20, rejection increase by 32% and 17% respectively where for NF-1, rejection increases only by 5% with increase of cross-flow rate from 300 L h−1 to 750 L h−1. Due to high porosity, NF-1 and NF-20 membranes get easily fouled by the concentration polarization effects at low cross-flow rates. 4.4. Effect of pH on fluoride rejection and permeate flux Fig. 5 shows that the fluoride separation increases from 12% to 98.5% for NF-1, 8% to 91.4% for NF-2 and 10% to 95% for NF-20 with increase of pH from 2.0 to 10.01. Such increase in pH also led to substantial enhancement of flux. For NF-1 membrane the increase was from 62 L h −1 m −2 to 158 L h −1 m −2 within the pH range. Such positive effects of pH on fluoride removal by nanofiltration have been observed in some earlier studies [20,30] also. The higher

Fig. 6. Effect of pH on membrane charge density for fluoride removal through NF1, NF2 and NF20 membranes.

121

rejection may be traced to dissociation of sodium fluoride into F − at its pKa value of 3.16. The number of free fluoride ions increases with increasing alkalinity leading to increasing retention of the fluoride ions by membranes due to Donnan exclusion mechanisms. This also suggests the positive role of steric effects on fluoride retention. Fluoride ions are more strongly hydrated because of high charge density and has a relatively large hydrated radius (0.352 nm) compared to other ions present in groundwater. So F − ions are strongly retained by tighter membranes as a result of steric exclusion [30].At high pH values, the membrane potential lower than the isoelectric point turns the membrane negatively charged one because of the loss of proton carboxyl that increased the fluoride rejection [31]. Apparent pore size of polyamide NF membranes also varies with solution pH [32]. On the other hand, the membrane charge density increases (Fig. 6) with increase in pH values which results in high fluoride retention by the membrane [33]. The increase of the membrane charge density facilitates fluoride rejection at a given permeates flux. The relation of rejection and flux with membrane charge density has been shown in Fig. 7. Increase of pH reduces viscosity of the solution and this may lead to turbulent flow of the solution over the membrane active surface which reduces the concentration polarization while increasing permeates flux. 4.5. Effect of initial concentration on fluoride rejection and permeate flux The experimental and model-predicted rejection data as presented in Fig. 8 show that with increase of initial fluoride concentration, rejection of fluoride decreases. For NF-1 membranes, fluoride retention decreases from 98.7% to 95% for increase of fluoride concentration from 5 ppm to 30 ppm. Up to 20 ppm of initial fluoride concentration, such decrease in rejection is not so significant, however, beyond 20 ppm, the rejection decreases significantly. As the effective charged membrane area is fixed, with the increase of salt concentration, the fixed charge on the active layer of the membrane gets partially neutralized by the counter ions of the electrolyte while decreasing the electrostatic interaction between the ions and the membranes. The model data corroborate quite well with experiment data. Fig. 9 shows adverse impact of high fluoride concentration on the permeate flux. High fluoride concentration in groundwater introduces a concentration polarization layer on the membrane thereby reducing the permeate flux. With the increasing feed concentration, the osmotic pressure also increases due to the ionic particles and consequently effective operating pressure on the membrane decreases. This results in drop in both solvent flux (water flux) and fluoride rejection [34]. Except for NF-2 the model

Fig. 7. Effect of membrane charge density on fluoride removal and permeate flux through NF1, NF2 and NF20 membranes.

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Fig. 8. Effect of initial fluoride concentration on fluoride rejection through NF-1, NF-2 and NF-20 membranes. Operating conditions: fluoride concentration range 5 ppm–30 ppm, pH—10.01, cross flow rate 750 L h−1, pressure—14 kgf cm−2, cross flow velocity 1.16 m s−1, temperature 308 K.

data of NF-1 and NF-20 are matched well. The model-predicted values on NF-2 did not corroborate well with the experimental results largely because of the bigger pores of this membrane (NF-2) compared to the other membranes and such pores get blocked by trapped solute particles not considered in the model. Membrane charge density also increases with increasing solute concentration and leads to better separation efficiency of fluoride. The relation of fluoride concentration and membrane charge density has been shown in Fig. 10. 4.6. Effect of transmembrane pressure on permeate pH The pH of the investigated groundwater was as high as10.01 which is far above the acceptable limit (7–8 pH). Thus in addition to fluoride removal, pH also needs to be taken care of for safe drinking water. Fig. 11 represents the effects of transmembrane pressure on pH of the permeate. In the present investigation, NF-1 membrane was chosen to be the best membrane and was used throughout the study. Investigation results show that the pH of the permeate decreases with increase in pressure. pH decreases from 9.2 to 7.2 with the increase

Fig. 9. Effect of initial fluoride concentration on permeates flux through NF-1, NF-2 and NF-20 membranes. Operating conditions: fluoride concentration range 5 ppm–30 ppm, pH—10.01, cross flow rate 750 L h−1, pressure—14 kgf cm−2, cross flow velocity 1.16 m s−1, temperature 308 K.

Fig. 10. Effect of initial fluoride concentration on membrane charge density through NF-1, NF-2 and NF-20 membranes.

of pressure from 5 kgf cm−2to 14 kgf cm−2. The alkaline ions responsible for high pH gets rejected by the membrane, decreasing the overall pH on the permeate side.

4.7. Effect of fouling on permeate flux with respect to operation time Due to the buildup of concentration polarization layer, membranes normally get fouled and that causes decline of permeate flux during long term operation. But with the use of flat sheet cross flow module, fouling can be largely eliminated by the sweeping action of fluid on membrane surface and this reduces the possibility of concentration polarization. Fig. 12 indicates the extent of decline in flux due to fouling with time. Decrease of flux with respect to time is observed to be minimum (14%) for NF-2 membrane and maximum (19%) for NF-20 membrane. Rejection performance was however, better for NF-1 membrane compared to the other membranes and the achieved volumetric flux was industrially acceptable. Considering purity of water, the NF-1 membrane was found to be the best membrane. SEM images of the NF-1 membranes before and after the filtration run have been presented in Figs. 13 and 14. The figures indicate that the membranes do not undergo significant morphological changes possibly due to the very flow pattern of the cross flow module. Reuse of these membranes after a thorough rinsing with 0.1(N) NaOH and 10 −2 molar HNO3 was possible every time without any significant flux decline indicating the reversible nature of the minor fouling that was taking place. The membranes were also sterilized

Fig. 11. Effect of transmembrane pressure on permeates pH through NF-1 membrane. Operating conditions: fluoride concentration 20 ppm, Pressure range 5–14 kgf cm2, feed pH 10.01, cross flow rate 750 L h−1, cross flow velocity 1.16 m s−1, temperature 308 K.

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Fig. 14. SEM image of NF-1 membrane after investigation. Fig. 12. Effect of fouling on permeates flux with respect to operation time through NF1, NF2 and NF20 membranes. Operating conditions: Operation time range 0–190 h, Fluoride concentration 20 ppm, pH 10.01, cross flow rate 750 L h−1, pressure—14 kgf cm−2, cross flow velocity 1.16 m s−1, temperature 308 K.

with 200 ppm NaOCl solution followed by rinsing with ultrapure water that reduces further fouling of the membrane. 5. Economic evaluation The techno economic analysis was carried out for a plant capacity of 10,000 L Day −1considering removal efficiency of fluoride by NF-1 to be 98% at 14 kgf cm −2 and the flux rate of NF-1 at 158 LMH. Investment cost has been calculated by standard empirical equations from the literature as proposed by Bruggen et al. [35]. Cost factor was calculated by six-tenth power rules and the components of the capital cost are described as below: Civil Investment ($): 112 Qf + 28 n Mechanical Cost ($): 88 Qf0.85 + 120 n Electro technical Cost ($): 1980 + (4.1 × Qf × ΔP) Membrane module Cost ($): 800 n The overall investment and operating costs have been presented in Table 6. The economic evaluation is based on the annualized capital

cost. Given the total investment, in $, for a production of Q m 3/year of permeate, annualized capital cost A in $/m 3, is A ¼ ðtotal investment  CRFÞ=Q where CRF is the capital recovery factor and may be expressed as CRF =i (1+ i)n/[(1+i)n −1], n being the project life and i is the interest rate. Assuming a project life n = 20 years and interest rate, i = 10%, the CRF computes to be 0.11.
 3 Annualized capital cost $=m

0:24


 3 Annualized operating cost $=m

0:93


 3 Total annualized costs ðinvestment þ operating costsÞ $=m

1:17:

The reflected annualized cost (based on Indian market conditions) for producing fluoride-free clean drinking water involving the proposed membrane based treatment technology is $1.17 per m 3. 6. Conclusion A mathematical model was developed for capturing transport phenomena during removal of fluoride from contaminated groundwater by cross flow nanofiltration. The linearized approach adopted in the modeling reduced computation time significantly. The model could successfully predict the performance of the system as reflected in relatively low relative error and high overall correlation coefficient. The composite polyamide nanofiltration membrane used in cross flow mode was not only successful in removing 98% fluoride from contaminated water but also reduced high pH of the water to the desired level while yielding a high flux of 158 L h−1 m 2. After the economic analysis of the system, it appears that such a system can be very promising in

Table 6 The investment and operating cost for a community based plant. Investment costs ($)

Fig. 13. SEM image of NF-1 membrane before investigation.

Civil investment Mechanical engineering investment Electro-technical investment Membrane module

Operating costs ($/Yr.) 210 820 2010 4800

Electricity cost Membrane cost Labor cost

200 1600 1080

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producing fluoride-free safe drinking water at a quite affordable cost. The study is expected to raise scale up confidence in the backdrop of rare implementation of membrane-based technology in removing fluoride from contaminated groundwater in the vast affected areas of the world. Nomenclature Ak Porosity of the membrane cw,i Concentration in membrane of ion i (mol m −3) cw,i,av Average concentration of ion i (mol m −3) Cp,i Concentration in permeate of ion i (mol m −3) CBC,F Bulk concentration of fluoride (mol m −3) Ds,i Hindered diffusivity of ion i (m 2 s −1) DBC,i Bulk diffusivity of ion i (m 2 s −1) F Faraday's constant (C mol −1) Hc,i Hindrance factor for convection of ion i Hd,i Hindrance factor for diffusion of ion i Js Solute flux (mol m −2 s −1) Jv,i Volumetric flux of ion i (m 3 m −2 s −1) k Boltzmann constant, 1.38066 × 10 −23 J K −1 kmass Mass transfer coefficient of fluoride ion, m s −1 L h −1 m −2 Liter per square meter hour L h −1 Liter per hour ppm Parts per million (mg L −1) Pei Peclet number of ion i, dimensionless Qf Feed entering in the tank (m 3.h −1) rp Effective pore radius (nm) rs,i Solute radius of ion i (nm) Rj,F Rejection of fluoride ions (%) R Universal gas constant (J mol −1 K −1) T Absolute temperature (K) t Operation time XDC Effective charge membrane density (mol m −3) zi Valence of ion i ΔP Applied pressure difference (kg cm −2) ΔPe Effective pressure difference, (kg cm −2) Δx Effective membrane thickness (m) η Dynamic viscosity of the solution (kg m −1 s −1) Φ Steric coefficient λi Ratio of solute radius to pore radius of ion i ΔΨd Donnan potential difference (V) Ψ Electric potential

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